Research Collection. Optimal design of planar metamaterials. Doctoral Thesis. ETH Library. Author(s): Fallahi, Arya. Publication Date: 2010
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1 Research Collection Doctoral Thesis Optimal design of planar metamaterials Author(s): Fallahi, Arya Publication Date: 2010 Permanent Link: Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library
2 DISS. ETH No OPTIMAL DESIGN OF PLANAR METAMATERIALS A dissertation submitted to the SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH for the degree of Doctor of Sciences presented by ARYA FALLAHI M.Sc, University of Tehran, Iran born February 11, 1982 citizen of Iran accepted on the recommendation of Prof. Dr. Christian Hafner, examiner Prof. Dr. Daniel Erni, co-examiner Dr. Philippe Lalanne, Directeur de recherche CNRS, co-examiner 2010
3 Abstract Metamaterials are artificial structures that are developed to exhibit electromagnetic properties, which are not found in nature. The most prominent method to realize such materials is to fabricate a periodic structure consisting of identical cells, which may consist of different dielectrics, metals and semiconductors. Activities to realize metamaterials are mostly around planar structures because of their compatibility with well-developed microelectronic fabrication techniques and possibility of integration in a planar platform. This thesis focuses on analysis and design of planar metamaterials at microwave frequencies. In this regime, a planar metamaterial may be in form of a frequency selective surface or an electromagnetic crystal slab. At the beginning, the classic periodic method of moments for the analysis of frequency selective structures is reviewed briefly and some examples are outlined. After this preparatory section, a numerical technique for the analysis of a new type of planar metamaterials, consisting of printed metal patches on a periodically inhomogeneous substrate, is presented. Such structures are more promising than traditional frequency selective surfaces because of the control over substrate properties. To analyze these structures, a series equation obtained from the coupled multiconductor transmission line model is solved by the method of moments in Galerkin s regime. Next, the developed MoM/TL technique is generalized for the analysis of geometries with periodic and anisotropic substrates. In each step, several examples are outlined and analyzed using the proposed method. Next, different groups of basis functions, which may be used in the moment method for our particular problems, are introduced. They are basically categorized in three main groups, namely subdomain, entiredomain and large overlapping subdomain basis functions. Through some examples, the advantages and shortcomings of each group are discussed in detail. The dispersion analysis of these geometries is the next considered topic. In the dispersion analysis one is interested in the guided modes along the planar structure rather than in the response to an external excitation. i
4 ii ABSTRACT After a brief review of the previously developed methods a new approach based on coupling energy to a perturbed metamaterial is introduced. In this method, solving the dispersion problem is transformed to solving a diffraction problem in conjunction with finding minima of the reflection spectrum. The computation cost to perform this method is so low that a fine scan of the frequencies is possible and highly accurate results can be obtained. Designing frequency selective surfaces is investigated afterwards. First, a thorough study is done to explore different aspects of the optimization problem. The efficiency of several optimizers is investigated and compared, which enables one to select those with best performance depending on the problem type. The selected optimizers are utilized to design artificial magnetic conductors and some radar absorbers. The designed radar absorbers are then fabricated, and measured to demonstrate that periodic inhomogeneities in the substrate result in promising improvements of the device properties. The last study concentrates on the analysis of semi-infinite periodic structures with planar symmetry, i.e. planar bulk metamaterials. A new concept based on impedance boundary conditions is developed for the simulation of diffraction from semi-infinite geometries. Subsequently, some planar bulk metamaterials consisting of metal and dielectric inclusions are simulated using this technique.
5 Zusammenfassung Metamaterialien sind künstliche Strukturen, welche elektromagnetische Eigenschaften aufweisen können, die in der Natur nicht vorkommen. Die vielversprechendste Methode, solche Materialien zu realisieren, besteht darin, ist eine periodische Struktur aus identischen Bauelementen anzufertigen. Die Bauelemente werden aus unterschiedlichen Dielektrika, Metallen und Halbleitern gefertigt. Forschungsansätze fokussieren meist auf planare Strukturen wegen ihrer einfachen Realisierbarkeit mit hochentwickelte Mikroeletronikfabrikationstechniken und wegen der Integrationsmöglichkeit in planaren Plattformen. Diese Dissertation fokussiert auf die Analyse und der Entwurf von planaren Metamaterialien im Mikrowellenfrequenzbereich. Ein solches planares Metamaterial kann entweder in Form einer frequenzselektiven Oberfläche, oder einer elektromagnetischen Kristallplatte realisiert werden. Zu Begin wird die klassische Momentmethode, die für die Analyse frequenzselektiver Strukturen entwickelt wurde, besprochen und einige Beispiele werden diskutiert. Nach diesem Vorbereitungsteil wird ein numerisches Verfahren für die Analyse einer neuen Gruppe planarer Metamaterialien vorgestellt. Neue künstliche Materialien entstehen, wenn ein periodisch inhomogenes Substrat mit periodisch angeordneten Metallisierungen bedruckt wird. Aufgrund der erreichten Kontrolle über die Eigenschaften des Substrats sind solche Strukturen vielversprechender als traditionelle frequenzselektive Oberflächen. Um solche Strukturen zu simulieren wird eine mathematische Reihe, die aus dem Model der gekoppelten Mehrfachübertragungsleitung erhalten wurde, nach der Galerkin- Momentmethode gelöst. Danach wird die entwickelte MoM/TL Methode für die Analyse von Geometrien mit periodischen und anisotropen Substraten generalisiert. In jedem Schritt werden mehrere Beispiele betrachtet und mit der vorgeschlagenen Methode analysiert. Anschliessend werden verschiedene Arten von Basisfunktionen der Momentmethode für das spezifische Problem evaluiert. Sie können grundsätzlich in drei Kategorien eingeteilt werden: Teilbereichsbasisfunktionen, Ganzbereichsbasisfunktionen und sogenannte Basisfunktionen für grosse überlappende Teilbereiche. iii
6 iv ZUSAMMENFASSUNG Durch einige Beispiele werden die Nachteile und Vorteile jeder Kategorie im Detail diskutiert. Als nächstes Thema wird eine Dispersionsanalyse durchgeführt, bei der - an Stelle der Reflexion oder Transmission - die geführten Moden entlang der planaren Struktur betrachtet werden. Nach einem kurzen Review der bisher entwickelten Methoden wird ein neues Verfahren vorgestellt, welches auf Energieeinkopplung in Metamaterialien mit leicht variirenden Parametern basiert. Bei dieser Methode wird das Dispersionsproblem gelöst, indem die Minima des Reflexionsspektrum gefunden werden. Dieses Spektrum ist durch die Lösung des Diffraktionsproblems gegeben. Der niedrige Rechenaufwand des Reflexionsspektrums ermöglicht einen hochauflösenden Scan und sehr präzise Ergebnisse. Danach werden frequenzselektive Oberflächen entworfen. Das Optimierungsproblem wird charakterisiert und die Effizienz mehrerer Optimierungsalgorithmen wird ausgewertet. Diejenigen mit der besten Funktionalität werden ausgewählt und für den Entwurf künstlicher magnetischen Leiter und Radarabsorber verwendet. Durch die Herstellung und Messung der entworfenen Radarabsorber wird gezeigt, dass die Existenz einer einfachen periodischen Inhomogenität innerhalb des Substrats zu signifikanten Verbesserungen führen kann. Die letzte Untersuchung fokussiert auf die Analyse von semi-infiniten periodischen Strukturen, beziehungsweise von planarem Bulkmetamaterial. Ein neues Konzept, basierend auf Impedanzrandbedingungen, wird für die Diffraktionsimulationen aus semi-infiniten Geometrien entwickelt. Planare Bulkmetamatialien, bestehend aus Metall oder dielektrischen Einschlüssen, werden mit diesem Verfahren simuliert.
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